// Replacement Exam: Scala Part
//=======================================
// Roman Digits and Numerals
abstract class RomanDigit
case object I extends RomanDigit
case object V extends RomanDigit
case object X extends RomanDigit
case object L extends RomanDigit
case object C extends RomanDigit
case object D extends RomanDigit
case object M extends RomanDigit
type RomanNumeral = List[RomanDigit]
// (1) First write a polymorphic function that recursively
// transforms a list of options into an option of a list.
// As soon as a None is inside the list, the result is None.
// Otherwise produce a list of all Some's appended.
//def optionlist[A](xs: List[Option[A]]): Option[List[A]] =
// some testcases
//optionlist(List(Some(1), Some(2), Some(3))) // -> Some(List(1, 2, 3))
//optionlist(List(Some(1), None, Some(3))) // -> None
//optionlist(List()) // -> Some(List())
// (2) Write a function first a function that converts a character
// into a roman digit (if possible). Then convert a string into
// a roman numeral (if possible). In both cases, if the conversion
// is not possible, the functions should return None.
//def Char2RomanDigit(c: Char): Option[RomanDigit] =
//def String2RomanNumeral(s: String) : Option[RomanNumeral] =
// some test cases
//String2RomanNumeral("IIII")
//String2RomanNumeral("IV")
//String2RomanNumeral("VI")
//String2RomanNumeral("IX")
//String2RomanNumeral("MCMLXXIX")
//String2RomanNumeral("MCMXLIV")
//String2RomanNumeral("M C M X L I V") // None
// (3) Write a recursive function RomanNumral2Int that converts a
// RomanNumeral into an integer.
//def RomanNumeral2Int(rs: RomanNumeral): Int =
// some test cases
//RomanNumeral2Int(List(I,I,I,I)) // 4
//RomanNumeral2Int(List(I,V)) // 4
//RomanNumeral2Int(List(V,I)) // 6
//RomanNumeral2Int(List(I,X)) // 9
//RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979
//RomanNumeral2Int(List(M,C,M,X,L,I,V)) // 1944
// (4) Write a function that converts a string (containing
// a roman numeral) into an integer (if possible). If
// this is not possible, the functions should return None.
//def String2Int(s: String): Option[Int] =
// some test cases
//String2Int("IIII") // 4 (though invalid roman numeral)
//String2Int("IV") // 4
//String2Int("VI") // 6
//String2Int("IX") // 9
//String2Int("MCMLXXIX") // 1979
//String2Int("MCMXLIV") // 1944
//String2Int("") // 0
//String2Int("MDCLXI") // 1661
//String2Int("MMMCMXCIX") // 3999
//String2Int("XLVIII") // 48
//String2Int("MMVIII") // 2008
//String2Int("MMXI") // 2011
//String2Int("MIM") // 1999
//String2Int("MCMLVI") // 1956
//String2Int("III") // 3
//String2Int("XXX") // 30
//String2Int("CCC") // 300
//String2Int("MMM") // 3000
//String2Int("VII") // 7
//String2Int("LXVI") // 66
//String2Int("CL") // 150
//String2Int("MCC") // 1200
//String2Int("IV") // 4
//String2Int("IX") // 9
//String2Int("XC") // 90
//String2Int("MDCLXVI") // 1666
//String2Int("VIV") // 9 (but should be written as IX)
//String2Int("IVX") // 14 (also invalid)
// error cases
//String2Int("I I I I")
//String2Int("MC?I")
//String2Int("abc")